School Superintendent ­Carol R. Johnson has recently been in discussions with the mayor and the School Committee about her need to be in ­Tennessee frequently to care for her ill husband, a circumstance that has raised questions about her continued tenure in her post.

“She wants to stay through the rest of the year, but who is to say? Her husband is sick,” said an official privy to discussions about her future.

Johnson, who makes $267,000 annually overseeing a department in the midst of tremendous change, has told ­Mayor Thomas M. Menino and School Committee chairman Michael O’Neill that she needs to spend her weekends in ­Memphis and possibly some additional days, depending on her husband’s health.

Johnson’s husband, ­Matthew, has been ill for several months, requiring some time in an intensive-care unit. At one point in the fall, John ­McDonough, the district’s chief financial officer, briefly stepped in as acting superintendent.

Matthew Wilder, a School Department spokesman, said Friday that Johnson has no plans to give up her job and that there have been no discussions of a resignation.

“There is no truth to the fact she is resigning,” Wilder said, addressing rumors swirling Friday that Johnson had given her notice.

“Anything beyond that would be pure speculation at this point,” he said.

Wilder also said there has been no talk about a formal leave of absence. “She did talk to the mayor about taking more time off than usual,” he said.

The official said Johnson is committed to staying in Boston while the School Department formulates a plan to overhaul how it assigns students to schools.

Work on that effort appears to be nearing the finish line. School officials presented three proposals last month to change the system to an external advisory committee. The panel was appointed by the mayor to weigh different options.

That committee could vote on recommendations this month. Johnson would then need to present the recommendations to the School Committee for a final vote, a process that would require at least two School Committee meetings and potentially some public ­forums.

It is unclear when the School Committee would have time to deliberate and vote on those recommendations, because it will probably be juggling another major task at the same time: On Wednesday night, Johnson will be presenting her proposed budget for the next school year.

The budget presentation will kick off a series of public hearings the School Committee will hold over the next few weeks that is expected to culminate with a final vote at the end of March.

Wilder said the School Committee and the mayor understand Johnson’s predicament.

“Family for everyone comes first,” Wilder said. “She is faced with a challenge with her husband who is in Memphis and her work being here.”